Solutions to All-Colors Problem on Graph Cellular Automata

Xiaoyan Zhang and Chao Wang

Complexity, 2019, vol. 2019, 1-11

Abstract:

The All-Ones Problem comes from the theory of - automata, which is related to graph dynamical systems as well as the Odd Set Problem in linear decoding. In this paper, we further study and compute the solutions to the “All-Colors Problem,†a generalization of “All-Ones Problem,†on some interesting classes of graphs which can be divided into two subproblems: Strong-All-Colors Problem and Weak-All-Colors Problem, respectively. We also introduce a new kind of All-Colors Problem, - Random Weak-All-Colors Problem, which is relevant to both combinatorial number theory and cellular automata theory.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:3164692

DOI: 10.1155/2019/3164692

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